If you incorporate or get an LLC, or any other business entity other than a sole propreitorship you will be required to submit a business name with that application. That requires making sure the name is not already used.
However, you do not need to start a formal business entity t reserve a trade or business name. You can start as a sole proprietorship and get a DBA (doing business as) or file a fictitious business name statement that shows you doing business under that specific name. Those forms usually run between $5 - $25 per registered name in most states.
Jason brings up a good point in his last comment as well. While the business name may be available, you also need to check general trade and copyrights. For example, you might be clear to register the company name "The Quicker Picker Upper" because that company doesn't exist in your state, but you can bet Bounty Paper towels will come after you for trademark infringement.
If you're looking for advice on starting a business check out www.thebizwizards.com.